Parameter Epsilon Research Articles

Charged KaonK→3π CP violating asymmetries at NLO in CHPT

We give the first full next-to-leading order analytical results in Chiral Perturbation Theory for the charged Kaon K \to 3 pi slope g and decay rates CP-violating asymmetries. We have included the dominant Final State Interactions at NLO analytically and discussed the importance of the unknown counterterms. We find that the uncertainty due to them is reasonable just for \Delta g_C, i.e. the asymmetry in the K^+ \to pi^+ pi^+ pi^- slope g; we get \Delta g_C = -(2.4 +- 1.2) 10^{-5}. The rest of the asymmetries are very sensitive to the unknown counterterms. In particular, the decay rate asymmetries can change even sign. One can use this large sentivity to get valuable information on those counterterms and on Im(G_8) coupling --very important for the CP-violating parameter epsilon'_K-- from the eventual measurement of these asymmetries. We also provide the one-loop O(e^2 p^2) electroweak octet contributions for the neutral and charged Kaon K \to 3 pi decays.

Isospin Violation inϵ′

On the basis of a next-to-leading-order calculation in chiral perturbation theory, the first complete analysis of isospin breaking for direct CP violation in K0-->2 pi decays is performed. We find a destructive interference between three different sources of isospin violation in the CP violation parameter epsilon'. Within the uncertainties of large-N(c) estimates for the low-energy constants, the isospin violating correction for epsilon' is below 15%.

Dielectric dispersion in Bi3Zn2Sb3O14 ceramic: a pyrochlore type phase

The electric and dielectric properties of Bi3Zn2Sb3O14 ceramic were studied by impedance spectroscopy. The measurements were performed in the frequency range 5 to 13 MHz and at temperature ranges from 25 to 700 °C. The permittivity was calculated by the variation of the imaginary part of the impedance (-Im(Z)) as function of 1/omega, where omega represents the angular frequency (2pif). The parameter epsilon = f(T) exhibits values in the range from 40 to 48. The dielectric losses (tandelta) show slight dependence with the temperature up to 400 °C. A strong increasing of the tandeltaoccurs at temperatures higher than 400 °C. In a general way, a decrease of the parameter tandelta occurs with the increasing frequency.

Non-periodic explicit homogenization and reduction of dimension: the linear case

The aim of this paper is to give explicit limit expressions, for diffusion equations involving a small parameter epsilon, describing both nonperiodic homogenization and reduction of dimension. In o ...

Noise-level estimation of time series using coarse-grained entropy.

We present a method of noise-level estimation that is valid even for high noise levels. The method makes use of the functional dependence of coarse-grained correlation entropy K2(epsilon ) on the threshold parameter epsilon. We show that the function K2(epsilon ) depends, in a characteristic way, on the noise standard deviation sigma. It follows that observing K2 (epsilon ) one can estimate the noise level sigma. Although the theory has been developed for the Gaussian noise added to the observed variable we have checked numerically that the method is also valid for the uniform noise distribution and for the case of Langevin equation corresponding to the dynamical noise. We have verified the validity of our method by applying it to estimate the noise level in several chaotic systems and in the Chua electronic circuit contaminated by noise.

Sources and holes in a one-dimensional traveling-wave convection experiment.

We study dynamical behavior of local structures, such as sources and holes, in traveling-wave patterns in a very long (2 m) heated wire convection experiment. The sources undergo a transition from stable coherent behavior to erratic behavior when the driving parameter epsilon is decreased. This transition, as well as the scaling of the average source width in the erratic regime are both qualitatively and quantitatively in accord with earlier theoretical predictions. We also present results for the holes sent out by the erratic sources.

Time scale of protein aggregation dictated by liquid-liquid demixing.

The growing impact of protein aggregation pathologies, together with the current high need for extensive information on protein structures are focusing much interest on the physics underlying the nucleation and growth of protein aggregates and crystals. Sickle Cell Hemoglobin (HbS), a point-mutant form of normal human Hemoglobin (HbA), is the first recognized and best-studied case of pathologically aggregating protein. Here we reanalyze kinetic data on nucleation of deoxy-HbS aggregates by referring them to the (concentration-dependent) temperature T(s) characterizing the occurrence of the phase transition of liquid-liquid demixing (LLD) of the solution. In this way, and by appropriate scaling of kinetic data at different concentrations, so as to normalize their spans, the apparently disparate sets of data are seen to fall on a master curve. Expressing the master curve vs. the parameter epsilon = (T - T(s)) / T(s), familiar from phase transition theory, allows eliciting the role of anomalously large concentration fluctuations associated with the LLD phase transition and also allows decoupling quantitatively the role of such fluctuations from that of microscopic, inter-protein interactions leading to nucleation. Referring to epsilon shows how in a narrow temperature span, that is at T - T(s), nucleation kinetics can undergo orders-of-magnitude changes, unexpected in terms of ordinary chemical kinetics. The same is true for similarly small changes of other parameters (pH, salts, precipitants), capable of altering T(s) and consequently epsilon. This offers the rationale for understanding how apparently minor changes of parameters can dramatically affect protein aggregation and related diseases.

Investigation of the quantum cantori regime in quarter-stadium billiards.

We study experimentally and numerically the regime of quantum cantori in quarter-stadium billiards. Experimentally, a quarter-stadium billiard is simulated by a thin quarter-stadium microwave cavity. Using a field perturbation technique and a circular wave expansion method we reconstruct the eigenfunctions of the quarter-stadium microwave billiard with the parameter epsilon =0.1 in the cantori regime N=7-63. The quarter-stadium billiards with epsilon =0.1 and 0.05, respectively, are also investigated numerically. We show that in the quantum cantori regime the rescaled localization length of the eigenfunctions fluctuates around a value that depends on the parameter epsilon.

Two-phase flow in correlated pore-throat random porous media

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter epsilon, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter e, the greater the deviation of the normalized size distribution of the invaded throat N-inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter epsilon. The velocity distribution f (alpha) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large alpha) is longer for a larger correlation parameter epsilon. For a smaller epsilon, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter e and the increase of the network size L-nz. E has a minimum as L increases up to the maximum no matter what the values of P, M and epsilon. The E similar to L-nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.

Signal enhancement in 5QMAS spectra of spin-5/2 quadrupolar nuclei.

5QMAS experiments on spin-5/2 systems display a low sensitivity compared with their 3QMAS counterparts. Nevertheless, the superior resolution of 5QMAS over 3QMAS makes these experiments a favorable choice for many materials. We report an enhancement scheme for the 5QMAS experiment, using an improved five-quantum excitation pulse scheme combined with a FAM-II conversion pulse. The results are verified experimentally on a polycrystalline sample of gamma-(27)Al(2)O(3), showing an enhancement factor of 2.4 over the simple two-pulse (CW) 5QMAS scheme. Numerical computations of the efficiency parameter epsilon support these results.

Wetting and structure of a fluid in a spherical cavity.

The equilibrium local densities, structure, and wetting of a one-component fluid in a spherical cavity, of variable radius R, are determined, using density-functional theory, as functions of two parameters characterizing the system: the radius R and the cavity/fluid potential parameter epsilon(W). The cavity acts as an external potential V(ext)(r) on the molecules of the confined fluid, the particles of which are of constant diameter d. The equilibrium density profile, as a result of strong confinement, develops peaks in the center of the cavity and/or close to the pore wall and, in certain situations, in other intermediate points; the cavity can also be liquid full, capillary condensation.

Probing neutrino nonstandard interactions with atmospheric neutrino data

We have reconsidered the atmospheric neutrino anomaly in light of the laetst data from Super-Kamiokande contained events and from Super-Kamiokande and MACRO up-going muons. We have reanalysed the proposed solution to the atmospheric neutrino anomaly in terms of non-standard neutrino-matter interactions (NSI) as well as the standard nu_mu -> nu_tau oscillations (OSC). Our statistical analysis shows that a pure NSI mechanism is now ruled out at 99%, while the standard nu_mu -> nu_tau OSC mechanism provides a quite remarkably good description of the anomaly. We therefore study an extended mechanism of neutrino propagation which combines both oscillation and non-standard neutrino-matter interactions, in order to derive limits on flavour-changing (FC) and non-universal (NU) neutrino interactions. We obtain that the off-diagonal flavour-changing neutrino parameter epsilon and the diagonal non-universality neutrino parameter epsilon' are confined to -0.03 < epsilon < 0.02 and |epsilon'| < 0.05 at 99.73% CL. These limits are model independent and they are obtained from pure neutrino-physics processes. The stability of the neutrino oscillation solution to the atmospheric neutrino anomaly against the presence of non-standard neutrino interactions establishes the robustness of the near-maximal atmospheric mixing and massive-neutrino hypothesis. The best agreement with the data is obtained for Delta_m^2 = 2.3*10^{-3} eV^2, sin^2(2*theta) = 1, epsilon = 6.7*10^{-3} and epsilon' = 1.1*10^{-3}, although the chi^2 function is quite flat in the epsilon and epsilon' directions for epsilon, epsilon' -> 0.

Universal scaling properties of type-I intermittent chaos in isolated resistance arteries are unaffected by endogenous nitric oxide synthesis

Spontaneous fluctuations in flow in isolated rabbit ear resistance arteries may exhibit almost-periodic behavior interrupted by chaotic bursts that can be classified as type-I Pomeau-Manneville intermittency. This conclusion was supported by the construction of parabolic return maps and identification of the characteristic probability distributions for the number of oscillations per laminar segment (n) associated with the type-I scenario. Pharmacological inhibition of nitric oxide (NO) synthesis by the vascular endothelium modulated the dynamics of the reinjection mechanism, and thus the generic shape of the probability distribution for n. Nevertheless, average laminar length was related to a derived bifurcation parameter epsilon according to power-law scaling of the form <n> approximately epsilon(beta), where the estimated critical exponent beta was close to the theoretical value of -0.5 both in the presence and absence of NO synthesis.

Effect of surface charges on the curvature moduli of a membrane.

The modification of the curvature moduli due to surface charges in lipid bilayers is analyzed using the nonlinear Poisson-Boltzmann equation for the relationship between the charge density and surface potential. An expansion in a small parameter epsilon, which is the ratio of the Debye length and the radius of curvature, is used. At low charge densities, previous results obtained from the Debye-Huckel approximation are recovered. At high charge densities, the corrections to the mean and Gaussian curvature approach constant values. The total energy of curvature for a symmetrically charged membrane becomes negative when the charge density is increased beyond a critical value, indicating that the membrane spontaneously forms vesicles. An asymmetry in the charge densities on the two monolayers that form the bilayer results in a spontaneous curvature, and the radius of curvature could be large compared to the Debye length when the asymmetry is small. The case of adsorbed charges is also considered, where there is a reduction in the chemical energy when a charge is adsorbed on the surface. At low charge density, the mean and Gaussian curvature are equal in magnitude and opposite in sign to that for fixed charges, while at high charge density, the mean and Gaussian curvature approach values identical to that for a surface with fixed charges. Numerical calculations of the change in the curvature moduli with realistic parameter values indicate that these effects are likely to be of importance in the spontaneous formation of vesicles.

Slow Release of Drug through Deformed Coating Film: Effects of Morphology and Drug Diffusivity in the Coating Film

The effects of the morphology and drug diffusivity in the coating film on the slow release characteristics have been analyzed numerically under the constraint that the volume of the coating film and the drug matrix is maintained constant. Two different systems of coated particles with deformed coating films were studied and their release characteristics compared with those of the coated particles having spherical coating films. The average release rate, fractional release, drug concentration profiles, and the initial burst of drug were found to be strongly influenced by the ratio of drug diffusivity in the coating film to that in the drug matrix D(r) (i.e., dimensionless drug diffusivity in the coating film). Increasing D(r) always increased the release rate, the fractional release, and the initial burst of drug, but reduced the initial lag times of drug release. The effect of shape deformation was very significant in the drug concentration profiles and the initial lag times; in contrast, it was not so substantial on the fractional release and the average release rates. The morphology difference in the deformed systems was also found to affect the release characteristics to different extents. Increasing the degree of the shape deformation, represented by the perturbation parameter epsilon, always reduced the effective surface area for the controlled release of drug. Because of the compensation effects between decreasing surface area and the non-uniform mass flux distribution, even though the heterogeneity of surface mass flux distribution would become more considerable, the effects of increasing shape deformation to the overall release rate would be less than expected unless the coating film was deformed significantly enough. The effect of the shape deformation and the morphology difference become less effective to differentiate the release characteristics with increasing D(r).

Master formulae for ΔF=2 NLO-QCD factors in the Standard Model and beyond

We present analytic formulae for the QCD renormalization group factors relating the Wilson coefficients C_i(mu_t) and C_i(mu), with mu_t = O(m_t) and mu < mu_t, of the Delta F=2 dimension six four-quark operators Q_i in the Standard Model and in all of its extensions. Analogous analytic formulae for the QCD factors relating the matrix elements <Q_i(2 GeV)> and <Q_i(mu_K)> with mu_K < 2GeV are also presented. The formulae are given in the NDR scheme. The strongest renormalization-group effects are found for the operators with the Dirac structures (1 - gamma_5)*(1 + gamma_5) and (1 - gamma_5)*(1 - gamma_5). We calculate the matrix elements <\bar K^0|Q_i|K^0> in the NDR scheme using the lattice results in the LRI scheme. We give expressions for the mass differences Delta M_K and Delta M_B and the CP-violating parameter epsilon_K in terms of the non-perturbative parameters B_i and the Wilson coefficients C_i(mu_t). The latter summarize the dependence on new physics contributions.

Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane.

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.

Backbone dynamics of the natively unfolded pro-peptide of subtilisin by heteronuclear NMR relaxation studies.

The dynamics of the natively unfolded form of the pro-peptide of subtilisin (PPS) have been characterized at two different pHs (6.0 and 3.0) by 15N relaxation experiments. 15N relaxation data is obtained at multiple field strengths and a detailed comparison of spectral density mapping, the model free approach and the recently proposed Cole-Cole model free (CC-MF) analysis is presented. The CC-MF analysis provides a better fit to the observed magnetic field dependence of 15N relaxation data of unfolded PPS than conventional model free approaches and shows that fluctuations in R2 may be accounted for by a distribution of correlation times on the nanosecond timescale. A new parameter epsilon derives from the analysis and represents the width of the distribution function and the heterogeneity of the dynamics on the nanosecond timescale at a particular site. Particularly interesting is the observation that epsilon is sensitive to pH changes and that PPS samples a wider distribution of nanosecond time scale motions at less acidic pHs than at more acidic pHs. These results suggest that PPS experiences a higher degree of correlated motion at pH 6.0 and that electrostatic interactions may be important for inducing correlated motions on the nanosecond timescale in unfolded PPS.

Phase turbulence in Rayleigh-Bénard convection

We present a three-dimensional simulation of Rayleigh-Benard convection in a large aspect ratio Gamma=60 with stress-free boundaries for a fluid Prandtl number sigma=0.5. We find that a spatiotemporal chaotic state (phase turbulence) emerges immediately above onset, which we investigate as a function of the reduced control parameter epsilon. In particular we find that the correlation length for the vertical velocity field, the time averaged convective current, and the mean square vorticity have power law behaviors near onset, with exponents given by -1/2, 1, and 5/2 respectively. We also find that the time averaged vertical velocity and vertical vorticity fields have the same (disordered) spatial characteristics as the corresponding instantaneous patterns for these fields, and that there is no long-term phase correlation in the system. Finally, we present simple theoretical explanations for the time averaged convective current as a function of the control parameter, and for the fact that the time dependence of three global quantities (characterizing the dissipation of kinetic energy, the release of internal energy by buoyancy, and entropy flow) is essentially the same.

Statistical significance of protein structure prediction by threading.

In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter epsilon that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter epsilon takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.